At t = 0 s a flywheel is rotating at 30 rpm. A motor gives it a constant acceleration of 0.6rads/s^2 until it reaches100 rpm. The motor is then disconnected. How many revolutions are completed at t = 24 s?

At t = 0 s a flywheel is rotating at 30 rpm. A motor gives it a constant acceleration of 0.6rad/s^2 until it reaches 100 rpm. The motor is then disconnected. How many revolutions are completed at t = 24 s?

The motor gives the flywheel a constant angular acceleration: a;
Then wf = w0 + a*t; here w0 is angular velocity 30 rpm at t = 0s, wf = 100 rpm. From this equation you can calculate the time it takes the flywheel to accelerate from 30 rpm to 100 rpm. You have to make sure that the units within equations are the same. Remember that:
1 rpm = (pi/30) rad/s, because one full turn, the same as the angle of 360 degrees, is 2*pi in radians;
then Ta = (wf-w0)/a = (100-30)*(pi/30) rad/s / 0.6 rad/s^2;
Is this time shorter or longer than 24 s?
After the motor is disengaged the wheel keeps rotating with a constant angular velocity. It Ta is shorter than 24s, then the total angle in radians completed by the flywheel at t=24s is:
u(t)=w0*Ta + a*((Ta)^2)/2 + wf*(Ta-24s); here the second term is for the constant angular velocity rotation after the motor is disconnected.
Divide it by 2*pi to find the number of revolutions.
If Ta is longer than 24s, then the angle in radians:
u(t) = w0*24s + a*((24s)^2)/2